Since the word between the inequalities is "and," we are looking for where the solution sets intersect.
Solution Set: Ø Graph:
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To solve the compound inequality, we will solve each of the inequalities separately and then graph them together. The intersection of these solution sets is the solution set for the compound inequality.
First Inequality
Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.
The second inequality is satisfied for all values of t that are less than or equal to 3.
Note that the point on 3 is closed because it is included in the solution set.
Compound Inequality
The solution to the compound inequality is the intersection of the solution sets. Notice that, the solution sets of the inequalities do not intersect, so the solution to the compound inequality is an empty set.
First Solution Set:& 3≥ t
Second Solution Set:& t≤ 4
Intersecting Solution Set:& Ø
Finally, we will draw the graph of the inequality as a line with no shaded parts.
